For those big logs, I would read them and see if it looks like something is wrong with apache and nginx and the logs are being flooded with error messages. If they are just really old, as Jaglover pointed out, they need to be rotated (emerge logrotate).

If you're not doing anything other than standard webserver / mysql / php stuff on this box, you may be better off with a managed server, if you're unwilling to learn how to set it up properly.

In the last four years I was able to do everything on the project except server administration. That's why I have a server admin for this. But he is in vacation. I know how to restart the system and how to change the nameserver ip to reroute the users to the backup server.

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If you're willing to learn, start with logrotate and mysql configuration especially regarding binary logs, which you may not need, provided you've set up a proper backup solution. You really have to know more about Linux to run a server.

100% agree. I bought some books at Amazon now and I will try to learn it.